O S THE COSTR.ACTIOY O F ;\IOLECULES I S T H E LIQUID STATE BT SEHGICS G. MOKHCSHIS
According to the van der Waals equation,' the molecules of a liquid exist under very high pressure (up to ten thousand atmospheres or even higher) and vie should therefore expect' that the molecules of gas mould undergo a contraction on passing into the liquid state. This hypothesis was put forward many years ago by T. W. Richards,? who has applied it not only to change of state but also to chemical reactions. I n this article the wvriter makes the tR-0 following assumptions in order t o calculate this contraction. I. I n the state of vapour or gas the molecules are spherical. I n the liquid state they have the shape of the hexahedral prism of 2. maximum volume that can be inscribed in a sphere. From this form the liquid molecule can further pass over into that of the honey-comb cell3-this latter having the same volume as the hexahedral prism but a smaller surface area. On the basis of these assuniptions the ratio of the volumes of the inolecule in the gaseous and liquid states can be calculated as follows. Let R = radiusof asphere r = edge of an inscribed hexahedral prism & v = volume of the prism. T h e n v = j.\/Fr? ~'Rz-i-2 Differentiating, we obtain as t'he condition for maximum value of v Substitute this value for r in equation of the sphere = v1 =
(I),
and divide through by the volume
4 .rrR3 3
Then
\'
-= v1
2
__ = .4i 4",'3
I n this expression u is now tho masiniuni volume of the inscribed prism, and we have here therefore a measure of the contraction of the molecule in passing from the gaseous to the liquid state. Of the two assumptions on which this calculation was based, the first follows a t once if Langmuir's view4 is correct, that each molecule possesses a surface energy by virtue of which its surface tends to a minimum. Such an idea is in fact made the basis of a structural theory of molecules by W Van der Kaals: "Die Iiontinuitlit des gasformigen und fliissigen Znstandes," (1889), T.W.Richards: J. Am. Chem. Soc., 46, 1419 ( 1 9 2 4 ) ; 47,731 ( 1 9 2 5 ) . Arw. Fuhrmann: ".Inwendungen der Infinitesimalrechnung in den Saturwissenschaften."Teil I , 1 7 5 (1900). Langmuir: Colloid Symposium Monograph, 3,48 ( 1 9 ~ 5 ) .
SERGIUB G. MOKRUSHIN
I582
Taylor' and by the founder of the kinetic theory. With regard to the second assumption on the other hand, there is lit'tle agreement concerning the form of the liquid molecules; van Urk? suggests a cubical packing, and Hildebrand3 a close hexahedral packing. The author's view that a honey-comb structure is most probable, is borne out by the fact that soap bubbles formed in a closed space assume such a structure in accordance with the principle of minimum surface area.4 Further justification is afforded for this second assumption on the basis of Ramsay and Shields' modification of the Eotvos equation,j together with an equation deduced by the writer in earlier papers.6 These equations are as follows :-
yS = J (Q - R T ) and y Ti = K (Tk where S
=
-T
=
JXi.. . . . . . . . . . . . . . (3) (Xokrushinj
- 6 ) . . . . . . . . . . . . . . . . . (4) (Ramsay & Shields)
total surface of vapour molecules
Q = total heat of evaporation and
X, = internal heat of evaporation.
S J - A, Dividing (3) by ( 3 ) F', = K (Tk-T-6)
If further v
=
'
" " " "
volume of one liquid molecule
vi = volume of one vapour molecule rl = radius ', ii ('
=
mass of one molecule
and d
=
density of the liquid
S
=
4.rrri2K and vi
111
i.e.
):(
s = .+.rr
I
=
2 7rrI3 3
TU'
. (6) ..................
i;j
Dividing (6) by ( 7 ) and comparing with ( j j we find that .. ,.
I
?
. , . . (8)
IT. Taylor: .Inn. I'hys. ( I O ) 1, 137 (1924);Phil. LIag., ( 6 )41, 8;; (1921). .\. Th. van Vrk: 1-erslag..ikad. \Yetenschappen Amsterdam, 3 4 , 3 5 1 ! .925).
Hildebrand: "Solubility." Am. Chem. SOC.Monographs, S o . 1 7 , I 1 2 (1924). -4m.Fuhrmann: Lac. cit. Eotvos: Ann. P l i p i k , 27, 448 ( 1 8 8 j ) ; Ramsay and Shields: J. C'llem. S o . , 63, 1089 ( I 893). S. Llokrushin: l'hil, LIag.,48, 7 6 j (19241; 2 . allg. anorg. Clieni., 153. 273 ; 1 9 2 G , .
COXTRACTION O F MOLECULES I N THE LIQUID STATE
I583
Rearranging and evaluating known terms we obtain the ratio
=
112'45
?;ow the value of
(Tk for by Trouton's Rule = 67Tk
(Tk
-xT Xi
= 1 1 2 ' 4 52),(
-:) -
2
......
. . . . . . . . . . . . . . , (9)
can be determined at the boiling point (Ts), = 19T,, and according to Guldberg and Waage T,
.56 3
to a first approximation
57 Further evidence is thus afforded that the molecules are contracted in the liquid state. Comparing this value, however, with the one obtained previously for the maximum contraction, it appears that a t the boiling point the honey-comb structure has not yet been assumed.
Summary I t has been shown that the molecules contracts on passing from the gaaeous to the liquid state, and that a change in shape is suggested from that of a sphere, first to that of a hexahedral prism, and finally to that of a honeycomb cell. The Geiieral Cheniistry Laboratory Polytechniclnsfit l i t e o j I ' m 1 Suerdlosk. Russia. d p r a l 7 , i92;.
